Daniel takes his two dogs, Pauli the Pointer and Newton the Newfoundland, out to

Question

Daniel takes his two dogs, Pauli the Pointer and Newton the Newfoundland, out to a field and lets them loose to exercise. Both dogs sprint away in different directions, while Daniel stands still. From Daniel's point of view, Newton runs due North at 4.40 m/s, but from Pauli's point of view, Newton appears to be moving at 2.10 m/s due East. What must Pauli's velocity relative to Daniel be for this to be true? Express your answer in terms of the x and y components if North is the y-direction and East is the x-direction, and then express your answer as a magnitude and an angle measured counter-clockwise from due East.

X Component: ?

Y Compenent: ?

Magnitude and Direction: ?

Angle of Magnitude and Direction counter-clockwise from due east: ?

Explanation / Answer

V( N,D) = 4.4 j

V(N,P) = 2.1 i

V(P,D) = V(N,D) - V(N,P) = 4.4 j - 2.1 i = -2.1 i + 4.4 j

so X Component = -2.1 m/s

     Y Component: = 4.4 m/s

     Magnitude = sqrt(2.1^2 + 4.4^2) = 4.875 m/s

      angle = 180 - tan^-1 4.4/2.1 = 115.5 degree from due east

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